I will present some recent work on the following problem: Given a "non-degenerate" one-dimensional family of orthogonal projections onto planes in 3-space, is the Hausdorff dimension of Borel sets generically preserved under almost every projection in the family? I will also discuss the problem of when projections have positive area, and a related problem for when projections onto lines have positive length. The proofs use decoupling inequalities from harmonic analysis. This talk is based on joint work with Shengwen Gan, Shaoming Guo, Larry Guth, Dominique Maldague, and Hong Wang.